Season the shrimp with salt and pepper. Set aside.
Bring 2 quarts of filtered water and 1 ½ tablespoons of kosher salt up to a boil. Placing a lid on the pot will heat the water quicker. Once up to a rolling boil, cook the pasta according to package directions for al dente.
While the pasta water is heating and the pasta is cooking, heat 1 tablespoon of butter and 1 tablespoon of oil in a large skillet over medium-high heat.
Once the butter is melted, add the shrimp in one layer (you may have to cook the shrimp in 2 batches adding more butter and oil as needed) and cook for about 2 minutes. Turn them over and cook for another 1 to 2 minutes, or until just cooked through. Set them aside on a plate. Cover loosely with foil to keep warm.
Lower the heat to low and add the garlic, stirring constantly for about 20 seconds. Do not allow the garlic to brown.
Add 2 cups of the heavy cream and sun-dried tomatoes. Increase the heat to medium, stirring, until the cream is hot, but do not bring up to a boil.
Add the spinach and stir frequently until wilted. Taste for seasoning and adjust. Be aware that the Asiago cheese does contain salt, so do not oversalt at this point.
Once the spinach is wilted., remove the skillet from the heat.
Add the cheese in 2 additions, stirring constantly, until the sauce is a creamy consistency.
Add the shrimp back to the pan, stir. Heat through on low heat so you do not overcook the shrimp. Taste once more and adjust salt and pepper as desired.
Pour into a large serving bowl or into individual bowls and garnish with chopped parsley and additional shaved Asiago cheese. Serve very warm.